Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
Advertisements
उत्तर
The direction ratios of the vector `hat"i" + 0hat"j" - hat"k"` are (1, 0, – 1)
The direction cosines of the vector `hat"i" + 0hat"j" - hat"k"` are
`1/sqrt(1^2 + 0^2 + (-1)^2), 0/sqrt(1^2 + 0^2 + (-1)^2), (-1)/sqrt(1^2 + 0^2 + (-1)^2)`
`1/sqrt(1 + 0 + 1), 0/sqrt(1 + 0 + 1), (-1)/sqrt(1 + 0 + 1)`
`(1/sqrt(2), 0, (-1)/sqrt(2))`
DIrection ratios = (1, 0, – 1)
Direction cosines = `(1/sqrt(2), 0, (-1)/sqrt(2))`
APPEARS IN
संबंधित प्रश्न
Find the direction cosines of the line
`(x+2)/2=(2y-5)/3; z=-1`
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Find the direction cosines of a line which makes equal angles with the coordinate axes.
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
Find the direction cosines of the sides of the triangle whose vertices are (3, 5, −4), (−1, 1, 2) and (−5, −5, −2).
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).
Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.
For every point P (x, y, z) on the x-axis (except the origin),
A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Find the direction cosines and direction ratios for the following vector
`3hat"i" + hat"j" + hat"k"`
If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c
If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`, find the magnitude and direction cosines of `vec"a", vec"b", vec"c"`
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.
A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.
If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l2 + m2 + cnl = 0 are parallel, then the positive value of c is ______.
